Grid Infrastructure for Domain Decomposition Methods in Computational ElectroMagnetics

The accurate and efficient solution of Maxwell's equation is the problem addressed by the scientific discipline called Computational ElectroMagnetics (CEM). Many macroscopic phenomena in a great number of fields are governed by this set of differential equations: electronic, geophysics, medical and biomedical technologies, virtual EM prototyping, besides the traditional antenna and propagation applications. Therefore, many efforts are focussed on the development of new and more efficient approach to solve Maxwell's equation. The interest in CEM applications is growing on. Several problems, hard to figure out few years ago, can now be easily addressed thanks to the reliability and flexibility of new technologies, together with the increased computational power. This technology evolution opens the possibility to address large and complex tasks. Many of these applications aim to simulate the electromagnetic behavior, for example in terms of input impedance and radiation pattern in antenna problems, or Radar Cross Section for scattering applications. Instead, problems, which solution requires high accuracy, need to implement full wave analysis techniques, e.g., virtual prototyping context, where the objective is to obtain reliable simulations in order to minimize measurement number, and as consequence their cost. Besides, other tasks require the analysis of complete structures (that include an high number of details) by directly simulating a CAD Model. This approach allows to relieve researcher of the burden of removing useless details, while maintaining the original complexity and taking into account all details. Unfortunately, this reduction implies: (a) high computational effort, due to the increased number of degrees of freedom, and (b) worsening of spectral properties of the linear system during complex analysis. The above considerations underline the needs to identify appropriate information technologies that ease solution achievement and fasten required elaborations. The authors analysis and expertise infer that Grid Computing techniques can be very useful to these purposes. Grids appear mainly in high performance computing environments. In this context, hundreds of off-the-shelf nodes are linked together and work in parallel to solve problems, that, previously, could be addressed sequentially or by using supercomputers. Grid Computing is a technique developed to elaborate enormous amounts of data and enables large-scale resource sharing to solve problem by exploiting distributed scenarios. The main advantage of Grid is due to parallel computing, indeed if a problem can be split in smaller tasks, that can be executed independently, its solution calculation fasten up considerably. To exploit this advantage, it is necessary to identify a technique able to split original electromagnetic task into a set of smaller subproblems. The Domain Decomposition (DD) technique, based on the block generation algorithm introduced in Matekovits et al. (2007) and Francavilla et al. (2011), perfectly addresses our requirements (see Section 3.4 for details). In this chapter, a Grid Computing infrastructure is presented. This architecture allows parallel block execution by distributing tasks to nodes that belong to the Grid. The set of nodes is composed by physical machines and virtualized ones. This feature enables great flexibility and increase available computational power. Furthermore, the presence of virtual nodes allows a full and efficient Grid usage, indeed the presented architecture can be used by different users that run different applications

Construction and Application of an AMR Algorithm for Distributed Memory Computers

While the parallelization of blockstructured adaptive mesh refinement techniques is relatively straight-forward on shared memory architectures, appropriate distribution strategies for the emerging generation of distributed memory machines are a topic of on-going research. In this paper, a locality-preserving domain decomposition is proposed that partitions the entire AMR hierarchy from the base level on. It is shown that the approach reduces the communication costs and simplifies the implementation. Emphasis is put on the effective parallelization of the flux correction procedure at coarse-fine boundaries, which is indispensable for conservative finite volume schemes. An easily reproducible standard benchmark and a highly resolved parallel AMR simulation of a diffracting hydrogen-oxygen detonation demonstrate the proposed strategy in practice

A Parallel Mesh-Adaptive Framework for Hyperbolic Conservation Laws

We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the time-dependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics (MHD) and similar models in plasma physics. Local mesh refinement is realized by the recursive bisection of grid blocks along each spatial dimension, implemented numerical schemes include standard finite-differences as well as shock-capturing central schemes, both in connection with Runge-Kutta type integrators. Parallel execution is achieved through a configurable hybrid of POSIX-multi-threading and MPI-distribution with dynamic load balancing. One- two- and three-dimensional test computations for the Euler equations have been carried out and show good parallel scaling behavior. The Racoon framework is currently used to study the formation of singularities in plasmas and fluids.Comment: late submissio

Quadtrees as an Abstract Domain

Quadtrees have proved popular in computer graphics and spatial databases as a way of representing regions in two dimensional space. This hierarchical data-structure is flexible enough to support non-convex and even disconnected regions, therefore it is natural to ask whether this datastructure can form the basis of an abstract domain. This paper explores this question and suggests that quadtrees offer a new approach to weakly relational domains whilst their hierarchical structure naturally lends itself to representation with boolean functions

A Flexible Patch-Based Lattice Boltzmann Parallelization Approach for Heterogeneous GPU-CPU Clusters

Sustaining a large fraction of single GPU performance in parallel computations is considered to be the major problem of GPU-based clusters. In this article, this topic is addressed in the context of a lattice Boltzmann flow solver that is integrated in the WaLBerla software framework. We propose a multi-GPU implementation using a block-structured MPI parallelization, suitable for load balancing and heterogeneous computations on CPUs and GPUs. The overhead required for multi-GPU simulations is discussed in detail and it is demonstrated that the kernel performance can be sustained to a large extent. With our GPU implementation, we achieve nearly perfect weak scalability on InfiniBand clusters. However, in strong scaling scenarios multi-GPUs make less efficient use of the hardware than IBM BG/P and x86 clusters. Hence, a cost analysis must determine the best course of action for a particular simulation task. Additionally, weak scaling results of heterogeneous simulations conducted on CPUs and GPUs simultaneously are presented using clusters equipped with varying node configurations.Comment: 20 pages, 12 figure